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The race for the Republican presidential nomination, which has been marked by a series of strange and surprising turns, has become really strange and surprising.

Actually, amazing.

As in, The Amazing Kreskin, the venerable showbiz mentalist who this week tried to capitalize on an opportunity to garner free publicity for his nightclub act by offering to meet with Herman Cain and the women accusing him of sexual harassment, and—through his fabulous powers of divination—determine who is telling the truth and who is lying like a rug.

“There’s a smile involved here,” the 76-year-old Kreskin (who legally changed his name from George Kresge) told me on Wednesday from his magic shack in Montclair, N.J. “I’m following in the footsteps of the gals and their lawyers, who are obviously publicity-minded. One of these gals”—former National Restaurant Association employee Sharon Bialek—“has one of the big show-business lawyers”—Gloria Allred. “Obviously,” Kreskin added in a tone of possible sarcasm, “she’s doing it for the dedication and commitment. I don’t mean to suggest she’s doing it for anything else.”

Kreskin, who claims to have aided law-enforcement authorities in solving more than 20 criminal cases, is proposing to meet individually with candidate Cain, whose recent troubles stem from his days in the 1990s running the restaurant lobby, along with Bialek and Cain accuser Karen Kraushaar, a Treasury Department official who also worked for Cain and received a $45,000 settlement after filing a complaint about his behavior. There are said to be at least two other aggrieved former restaurant association employees who have yet to go public with their accounts of alleged come-ons. (Cain has denied wrongdoing.)

Given his amazing powers of perception and prophesy, I asked Kreskin if he would hazard a prediction concerning the responses of the women and the candidate to his kind offer.

“I would be stunned if they accepted,” the mind-reader told me, adding that he is so sure of himself that he bet three friends $1,000 each that his proposal would be spurned by the parties involved.

It turns out that Kreskin’s prediction is spot-on, at least regarding the women if not the candidate, whose spokespeople are very busy these days and didn’t get back to me by deadline. (Ordinary mortals can never know how the capricious Cain might react in any given situation, so it remains to be seen if Kreskin gets to keep his money.)

Kraushaar’s attorney, Washington labor lawyer Joel Bennett, said of Kreskin’s offer: “I would never recommend that to a client. It sounds like utter nonsense, to be honest with you.”

Allred, meanwhile, dismissed the offer with an uncharacteristically terse “No.” She added: “My client is prepared to testify under oath and she has corroboration of many of her points. We think that Mr. Cain should also testify under oath.”

Kreskin, whose salad days were four decades ago when he made 61 appearances on The Tonight Show (and apparently served as the inspiration for Johnny Carson’s recurring character Carnac the Magnificent), offered a suitably historic quip: “I have nothing against lawyers. I just wish all of them had been on the Titanic.”

Kreskin said his offer was prompted not only by his desire to stage a publicity stunt, but also by his disappointment that Cain seemed at one point to be amenable to taking a polygraph test. “Polygraph tests are unscientific,” Kreskin declared. “I can train many people to beat one.”

He said that if Cain’s accusers had only agreed, he could have determined the accuracy of their memories by sitting down with them and listening to their stories—“and at the end of that I would say whether I think they’re lying or telling the truth.”

Although Kreskin was right about the reaction of the women and their lawyers, he scored less well on such elementary questions as “What am I wearing?”—he simply laughed and refused to answer my query—and even felt it necessary to ask where I was calling from and whether I was taping our little chat.

“Don’t you know?” I inquired.

He cluelessly laughed again.

On safer ground, Kreskin predicted that he probably wouldn’t run into Cain when he ventures into the first primary state on Saturday and plays the Rochester Opera House in Rochester, N.H.

“The problem with Herman Cain is this,” Kreskin said. “Let’s say it turns out he’s lying. He loses credibility with his followers. But if it turns out he’s telling the truth, he’s not in the right business because that doesn’t work in politics.”